I am a complete novice when it comes to astronomy, but someone asked me the above question casually. It seems as though planets are all roughly spherical, whereas other celestial bodies aren't necessarily. Is there are particular reason for this?

3 Answers
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That's mainly because of the gravity, and of size. Small objects, e.g. a stone, create only a very weak gravitation. The stone is much harder than necessary to withstand this force caused by its own gravity.

Earth is much larger. The gravity at the surface causes the weight we feel. A huge mountain on Earth would be flattened under its own weight, because the matter it's made of isn't hard enough to withstand this weight.
By hills filling up valleys the planet as a whole becomes spherical.

When a planetary system is born, most material to build bodies is in fine dust(gas state/plasma) because it has termo-dynamic high , thus is easy that gravity force create regular spherical forms width very weight materials as iron (earth center) after that system planetary is yougest (lower termo-dynamic),it has planets and smal bodies with regular forms but with trajectory collision, after has collisions occurred , it has regular and irregular bodies, when it reach state like as solar system, it has regular forms(spherical) semi-regular(with flat surface but irregular form as phobos) and irregular (asteroids),

Other razons:

because the main axis force from Centripetal force of solar system, has a direction to west-east axis (earth)

Some bodies(planets and satellites) has liquid state matter and this dragg solid matter in her surface

If the planet was made of gas or liquid, and was not spinning it would be a perfect sphere, because with each atom settling as close to the center as possible, that's the shape you get. We can see this on Earth whenever we take a ride in a boat and look out at the ocean. We see the surface of a sphere. (If the planet is spinning, it bulges out around the equator a bit.)

A rocky planet like Earth is a bit more complicated than a gas or water world (but only a bit). Continents are lighter than the mantle, so they float in it, but they're rigid, so they can "stick up" a bit like a boat in water, rather than form a smooth layer over the mantle like oil on water.